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Author: Marta Sved
Publisher: American Mathematical Soc.
ISBN: 1470457288
Category : Mathematics
Languages : en
Pages : 201
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Book Description
Author: Marta Sved
Publisher: American Mathematical Soc.
ISBN: 1470457288
Category : Mathematics
Languages : en
Pages : 201
Get Book Here
Book Description
Author: Thomas Q. Sibley
Publisher: The Mathematical Association of America
ISBN: 1939512085
Category : Mathematics
Languages : en
Pages : 586
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Book Description
Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.
Author: Isaak Moiseevich I︠A︡glom
Publisher: Ishi Press
ISBN: 9784871878364
Category : Mathematics
Languages : en
Pages : 237
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Book Description
I. M. Yaglom has written a very accessible history of 19th century mathematics, with emphasis on interesting biographies of the leading protagonists and on the subjects most closely related to the work of Klein and Lie, whose own work is not discussed in detail until late in the book. Starting with Galois and his contribution to the evolving subject of group theory Yaglom gives a beautiful account of the lives and works of the major players in the development of the subject in the nineteenth century: Jordan, who was a teacher of Lie and Klein in Paris and their adventures during the Franco-Prussian War. Monge and Poncelet developing projective geometry as well as Bolyai, Gauss and Lobachevsky and their discovery of hyperbolic geometry. Riemann's contributions and the development of modern linear Algebra by Grassmann, Cayley and Hamilton are described in detail. The last two chapters are devoted to Lie's development of Lie Algebras and his construction of the geometry from a continuous group and Klein's Erlanger Programm unifying the different approaches to geometry by emphasizing automorphism groups. These last pages are definitely the climax of the book.
Author: Wladimir-Georges Boskoff
Publisher: Springer Nature
ISBN: 303154823X
Category :
Languages : en
Pages : 556
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Book Description
Author: Owen Byer
Publisher: American Mathematical Soc.
ISBN: 0883857634
Category : Mathematics
Languages : en
Pages : 485
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Book Description
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Author: Ton Marar
Publisher: Springer Nature
ISBN: 3031074424
Category : Mathematics
Languages : en
Pages : 124
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Book Description
This book draws on elements from everyday life, architecture, and the arts to provide the reader with elementary notions of geometric topology. Pac Man, subway maps, and architectural blueprints are the starting point for exploring how knowledge about geometry and, more specifically, topology has been consolidated over time, offering a learning journey that is both dense and enjoyable. The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories that explain the Cosmos. Geometry from Felix Klein's point of view is then presented, paving the way to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, as well as hypersurface models. Adopting a style that is both rigorous and accessible, this book will appeal to a broad audience, from curious students and researchers in various areas of knowledge to everyone who feels instigated by the power of mathematics in representing our world - and beyond.
Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486141705
Category : Mathematics
Languages : en
Pages : 578
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Book Description
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Author: Jordan Ellenberg
Publisher: Penguin
ISBN: 1984879065
Category : Mathematics
Languages : en
Pages : 481
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Book Description
An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.
Author: Stefan Schadwinkel
Publisher: Lulu.com
ISBN: 1411636147
Category : Body, Mind & Spirit
Languages : en
Pages : 111
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Book Description
This book unfolds a non-dualistic world view, a view of Unity. That view is applied to topical scientific and philosophical issues, like Time, the Brain, Chaos and Order, the Human Immune System and Quantum Physics. It is a practical guide to navigate around common scientific, philosophical and spiritual pitfalls. With powerful, inspiring lyric and vivid metaphors, the reader is guided to realize and engage the full human potential. Awe inspiring sacred geometry is described and very advanced Mer-Ka-Ba activation techniques are unveiled. The nature of Mer-Ka-Ba fields is explained and related to the universe as a whole. Connecting the eternal teachings of the ancient masters with state of the art quantum mechanics, the book is the perfect add-on to all systems of co-creation. If you have been delighted by movies like "What the bleep do we know ?!," then this book will open the gates to the mystery right before your eyes. Fasten your seatbelt and get ready for your Journey into the Art of the Universe.
Author: Judith V. Grabiner
Publisher: MAA
ISBN: 0883855720
Category : Mathematics
Languages : en
Pages : 307
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Book Description
An inspiring collection of a historian's work on the history of mathematics.
